contoh soal dan jawaban transformasi laplace
DESCRIPTION
pembahasan transformasi laplace melalui soal - soalTRANSCRIPT
Jawaban contoh soal Transformasi Laplace
1. Hitung: L [10 sin 4t + 4t2]
Jawab:
L [10 sin 4t + 4t2] = ]4[]4sin10[ 2tLtL
= ][4]4[sin10 2tLtL
= 10. 322
)3(.4
4
4
ss
= 32
!2.4
16
40
ss
= 32
8
16
40
ss
2. Hitung : )]4sin2(sin[ 5 tteL t
Jawab :
)1].......(4sinh[]2sin[)]4sinh2(sin[ 555 teLteLtteL ttt
4)5(
2]2sin[
2
5
steL t
= 42510
22 ss
= 2910
22 ss
……………….(2)
16
4]4[sinh
2
stL
16)5(
4]4sinh[
2
5
steL t
=162510
42 ss
=910
42 ss
………………(3)
Sehingga persamaan (2) dan (3) disubstitusikan pada persamaan (1), sehingga
)]4sin2(sin[ 5 tteL t = 2910
22 ss
- 910
42 ss
4
2]2[sin
2
stL
3. Hitung : )]([ tFL , jika F(t) =
3,0
3,0,5
t
t
Jawab:
0
)()]([ dttFetFL st
=
3
3
0
.0..5. dtedte stst
= dte st .5.
3
0
=
3
0
5 dte st
= 3
0]5 stes
= )1(5 3ses
4. Hitung : )]([ tFL , jika :
3/2,0
3/2),3/2cos()(
t
tttF
L[F(t)] = dttFe st )(0
= dttedte stst )3/2cos(.0.3/2
3/2
0
= dtte st )3/2cos(3/2
Subs. )3/2( tu , du = dt
Batas integrasi, ut
03/2 ut
L[F(t)]
0
)3/2( cosudue us
=
0
3/2 cosuduee st
= ][cos3/2 uLe
= 1
.2
3/2
s
se
= 12
3/2
s
se
5. Hitung : ])4
[( 2tL !
Jawab:
3
2 )3(][
stL
= 3
!2
s
= 3
2
s
L[(4
1) 2 ] = 4 .
3)4/1
(
2
s
= 33.4
8
s
= 38
1
s